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# LAst year the 5 employees of company x took an average of 16

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LAst year the 5 employees of company x took an average of 16 [#permalink]  17 Mar 2011, 18:03
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Difficulty:

35% (medium)

Question Stats:

85% (01:58) correct 15% (00:45) wrong based on 13 sessions
LAst year the 5 employees of company x took an average of 16 vacations days each.what was the average no of vacations taken by the same employees this year?

1. 3 employees had a 50% increase in their no of vacation days and 2 employes had a 50% decrease.
2. 3 employees had 10 more vacation days each and 2 employees had 5 fewer vacation days each.

Pls explain why the answer is B.

I think answer should be D.
[Reveal] Spoiler: OA

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Last edited by AnkitK on 17 Mar 2011, 18:33, edited 1 time in total.
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Re: mean DS [#permalink]  17 Mar 2011, 18:23
We know the total days taken last year is 16x5=80. We must find the new total days now.

(1) is not enough as we have no information as to how many vacation days were taken by the 3 that had an increase or the 2 that had a decrease. Don't be misled by the average being 16 and assume that they all took 16. As we dont know, we dont know what absolute number effect these changes will have, and this question is all about absolute numbers.

(2) This is better, we have absolute numbers. If as you say the OA is B, then there is clearly a typo either on your behalf or theirs as we are only told about 4 employees' absolute change and nothing of the 5th. For the answer to be B, one of the "2's" has to be a "3".

Assuming it is written correctly, then we have to consider C before E. We see that for those that increased to be a "50% increase", the two must have gone from 20->30, and the other two from 10->5 for it to be a 50% decrease. Therefore the remaining worker started with (80-20-20-10-10=)20 days, and increased 50% (as 3 workers increased) to 30, and so the answer is (C).
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Re: mean DS [#permalink]  17 Mar 2011, 19:58
E1 + E2 + E3 + E4 + E5 = Total = 5*16 = 80

From (1), it's not clear which of the employees had the increase and decrease and without knowing the exact number of leaves taken by each employee, we can't increment it accurately.

From (2), regardless of any employee taking any number of leaves, It will be Total + 30 - 10 = 80 + 10 = 90

Hence the average this year = 90/5 = 18, so the answer is B.
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Re: mean DS [#permalink]  17 Mar 2011, 20:13
Yes, OP msged me that there was in fact a typo on his behalf, which he has now edited, and so it is (B). It was a more interesting question though WITH the typo.
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Re: mean DS [#permalink]  18 Mar 2011, 18:44
@subhashghosh this year's average is 20 not 18 sorry being nosy

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Re: mean DS [#permalink]  18 Mar 2011, 19:39

Perhaps in real exam I would not proceed to calculate the actual value in DS questions.
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Re: mean DS   [#permalink] 18 Mar 2011, 19:39
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